There are concerns that climate-related physical and political risks are not yet properly reflected in asset prices. To address these concerns, we develop a dynamic asset pricing framework with rare disasters related to climate change. The novelty of this paper lies in linking carbon emissions and portfolio composition with the stochasticallyvarying probability of these events. Using theory and simulations we study the implications of the imminent threat of climate change on different market measures and on the participation of carbon-intensive assets in the aggregate portfolio, as well as the conditions that lead to these assets becoming stranded. Our result suggest that climate change implies a positive and increasing risk premium, with the overall equity premium depending on the volatility of the stochastic process that governs climate change risk. Transition risks lower substantially the participation of carbon intensive assets in the market portfolio, which should be fully de-carbonized by the end of the century for the worst IPCC emissions scenario.